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Conference Paper

Fast Computation of Graph Kernels

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Vishwanathan, S., Borgwardt, K., & Schraudolph, N. (2007). Fast Computation of Graph Kernels. In B. Schölkopf, J. Platt, & T. Hoffman (Eds.), Advances in Neural Information Processing Systems 19 (pp. 1449-1456). Cambridge, MA, USA: MIT Press.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-CBDF-8
Using extensions of linear algebra concepts to Reproducing Kernel Hilbert Spaces (RKHS), we define a unifying framework for random walk kernels on graphs. Reduction to a Sylvester equation allows us to compute many of these kernels in O(n3) worst-case time. This includes kernels whose previous worst-case time complexity was O(n6), such as the geometric kernels of G¨artner et al. [1] and the marginal graph kernels of Kashima et al. [2]. Our algebra in RKHS allow us to exploit sparsity in directed and undirected graphs more effectively than previous methods, yielding sub-cubic computational complexity when combined with conjugate gradient solvers or fixed-point iterations. Experiments on graphs from bioinformatics and other application domains show that our algorithms are often more than 1000 times faster than existing approaches.